Originally Posted by toThinkistoBe

If you want to get technical, you could use this equation:

F = 1/2pv^2(Cd)A
or
F = 1/2 p(v1+vw)^2(Cd)A


Where...
p is the density of air
v is your velocity relative to the air which would be your velocity plus the velocity of a head wind
v1 is your velocity
vw is head wind velocity
Cd is the drag coefficient which would be very hard to calculate. Its a constant that is between 0 and 1. 1 being the case where all the air stops when it hits you. If I had to guess I'd say for a rider in the drops it would probably be close to .2-.3, maybe lower.
A is the area of the orthographic projection of your body. that would be very difficult to calculate so to simplify (and introduce some more error) you could try just using your surface area.

This will give you the force applied by wind resistance (drag).

If you assume a constant velocity of 15mph (~6.7m/s), and take the density of air to be 1.204 kg/m^3 you can calculate the difference in force required based on different head wind speeds.

So, for 15mph bike speed and 0mph wind speed you get:
Fdrag1 ~ 27*A*(Cd)
and for 15mph bike speed and 15mph head wind you get:
Fdrag2 ~ 81*A*(Cd)

Then using P=F*v
change in P = (change in F)*v
or
change in P = (81-27)*A*Cd*v
since power is measured in Joules per second, you can find the number of extra calories required since 1 Joule is .239 calories. Keep in mind that the calories you are talking about are actually kilocalories or 1000 calories.

so the extra work required between 0 wind speed and 15mph head wind when traveling at 15mph:
W = 54*A*Cd*v*t
to account for the calories you are looking for:
W = 54*A*Cd*v*t*.239/1000
or
W = .0129*A*Cd*v*t
also, since velocity times time is distance, you can say:
W = .0129*A*Cd*x
So for traveling 10 miles (16093 meters) the extra work needed would be:
W = 207*A*Cd
If we assume Cd is very low (.2):
W = 41.4*A
If we assume Cd is higher (.3):
W = 62.1*A
and once more when Cd is .5:
W = 103.5*A

so, assuming I didn't make any calculation errors (its pretty late and I should be in bed) over a 10 mile ride, traveling at 15mph, you would burn 40-100 (times your area) more calories if there is a direct head wind of 15mph compared to no wind.

So, change out the total mileage, your speed, and head wind speed (be sure to convert to meters and meters per second) and you should have about as accurate a value (well a range, but close enough) as you can get without some ridiculous equipment.